No social security number
When filing an SS-4 for with the IRS (the form using which one obtains an EIN) the IRS requires listing a company representative and his/her/its tax ID number. Tax ID number can be SSN, EIN, or ITIN (individual tax ID given to foreign individuals with no SSN).
If you want to be the representative on file, and have SSN, you must use it. If you don't have SSN or ITIN you can file without listing any tax ID, provided you will obtain ITIN next time you file company tax return, if its will be required at the time of filing. We provide the service of obtaining EIN regardless of whether you have SSN or not, you can order it here: Obtaining EIN.